Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography

Abstract

In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and real part is the quantum metric tensor. Here, we propose and experimentally implement a complete Bloch state tomography to directly measure eigenfunction of an optical Raman lattice for ultracold atoms. Through the measured eigenfunction, the distribution of the complete QGT in the Brillouin zone is reconstructed, with which the topological invariants are extracted by the Berry curvature and the distances of quantum states in momentum space are measured by the quantum metric tensor. Further, we experimentally test a predicted inequality between the Berry curvature and quantum metric tensor, which reveals a deep connection between topology and geometry.

References in corpus (3)

• An Aharonov-Bohm interferometer for determining Bloch band topology
• Topological Euler class as a dynamical observable in optical lattices
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

Cited by in corpus (28)

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• Local geometry and quantum geometric tensor of mixed states
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• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Quantum Geometry and the Hidden Scales in Materials
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
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• Structure factors and quantum geometry in multiband BCS superconductors
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• Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Quantum process tomography of structured optical gates with convolutional neural networks
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• Detecting degenerate bands topological invariants in optical lattice
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
• Evolution of quantum geometric tensor of 1D periodic systems after a quench
• Proposal for realizing and probing topological crystalline insulators in optical lattices